I believe (when I read CP 5.291 carefully) that a sensation, insofar as it is recognized as such in an interpretive process, is already a semiosic phenomenon and functions as a hypothesis; but, as pure feeling, “a mere feeling of a particular sort, it is determined only by an inexplicable, occult power; and so far, it is not a representation, but only the material quality of a representation” (emphasis mine). “A feeling, therefore, as a feeling, is merely the material quality of a mental sign” (emphasis in original). What does the material quality of a mental sign mean?
It means, I believe, that if I do not consider the word dog as a sign (and therefore, we would argue today, as a composite of expression and content, or signifier and signified), but consider only the phonation dog as it can be physically recorded and played back by someone who does not know English, I find myself faced with the material quality of the sign (the substance of the expression, so to speak), but not yet with the semiotic phenomenon developed and concluded in a representation and an act of cognition. The feeling, then, is not yet a hypothesis but the material occasion offered me or offered to my brain as a stimulus provided to allow it to proceed to the inference. “The hypothetic inference of the sensation is two-thirds written (the premises) by the nature of our sensorial system: it is a hypothesis, but our conscious intervention is limited simply to drawing the conclusion, which is obtained in an automatic manner.… The laws of logic construct the form of the sensation, but its content, that which arrives from without, is not part of it: the feeling is the material quality of the perceptual sign” (Proni 1990: 106).
I believe it is possible to reconcile this idea of the sensation as priman with a nonintuitionist theory of all knowledge as inference. Provided that what I assume to be the initial sensation or stimulus is recognized as such, at the molar level, in the respect and capacity of something that interests me at that moment, independently of all cosmological considerations.
15.5. Peirce and the Tortoise
When reading Peirce, we must not confuse cosmology and gnoseology. As I already remarked in K & P, two different but mutually interdependent perspectives are interwoven in Peirce’s thought: the metaphysical-cosmological and the cognitive. Unless we read them in a semiotic key, Peirce’s metaphysics and cosmology remain incomprehensible. But we would have to say the same thing of his semiotics with respect to his cosmology. Categories such as Firstness, Secondness, Thirdness, and the concept of interpretation itself not only define modi significandi, that is, the ways in which the world can be known: they are also modi essendi, ways in which the world behaves, procedures through which the world, in the course of evolution, interprets itself. In K & P, I cited Mameli (1997: 4): “Given that Peirce thinks and demonstrates that intelligibility is not an accidental characteristic of the universe, that it is not, that is, a mere epiphenomenon of how things are, but a characteristic that ‘shapes’ the universe, it follows that a theory of intelligibility is also a metaphysical theory of the structure of the universe” (K & P, p. 399, n. 28). The theory of intelligibility and metaphysical theory, however, must sometimes be kept separate.
Kant said that the fact that we believe we know things on the basis of the mere evidence of our senses depends on a vitium subreptionis or subreption: we are so accustomed from childhood to grasp things as if they appeared to us already given in intuition that we have never thematized the role played by the intellect in this process. Therefore even what were for him empirical intuitions were already the result of a work of inference.
We can construct a semiotics without a subject or (what amounts to the same thing) in which the subject is everywhere. In this semiotics there will never be a priman because interpretation will proceed by mise en abyme. But, if from the cosmological point of view the inferential process is infinite, because there are no intuitions, we cannot ignore the cognitive instance, that is, that edge of the semiosis that is formed when a subject (any instance capable of saying I that somehow enters into the semiosis from the material and corporal outside—what I am speaking about is a brain) installs itself and touches off a chain of inferences under the stimulus of something that, from its own point of view and only in this precise spatiotemporal segment, attracts its attention.7 The I in this case stands on that edge where on the one hand there stands, let’s say, the dog—the thing that interests him at that moment—and on the other hand, everything else—which does not interest him.
In this phase Firstness, as we saw, is a presence “such as it is,” nothing but a positive characteristic, like a purple color perceived without any sense of the beginning or the end of the experience, without any self-awareness separate from the sensation of the color; it is a potentiality without existence, the simple possibility of a perceptual process. In order to contest these qualia that precede any inference, we must take as our point of departure the principle that they constitute an intuitive moment, without our being able to conceive of further inferential processes behind it, in a sort of infinite fractalization. But I would like to remind the reader that the infinite fractalization of a sea coast does not prevent a human subject, who has a molar view compared with the molecular view of an ant, from covering in a single step what would be for the ant an extremely long and tortuous trajectory.
We are back, if you will, to the paradox of Achilles and the tortoise, in which we must take into account the distinction between potential infinity and infinity in act, already present in Aristotle.
In the paradox Achilles must first cover half the distance, but before that he must cover a quarter, and before that an eighth, and so on ad infinitum, so that he will never succeed in catching up with the tortoise. It has been observed, however, that, although this process of fractalization can continue infinitely, its result will never be greater than one—as occurs in any case with irrational numbers, so that 3.14, however successful we may be in analyzing it, will never be 4.
If we apply this argument to the fractal length of a coast, where the potential process of division could be infinite, at least insofar as we can always postulate smaller and smaller microbes, this does not prevent Achilles in practice covering this space with a single stride. Achilles will cover a unit of distance appropriate to him in a unit of time appropriate to him.
Already Aristotle (Physics III, 8, 206) objected to Zeno that, among magnitudes, there exists infinity by addition (I can always find an even number greater than the preceding one) but not by division, insofar as the infinity of the subintervals into which a unit of length is divisible is always contained in a limited totality (never greater than one) which may constitute the object of an empirical intuition.
In other words, if, cosmologically speaking, there is never perhaps a Firstness that is not the result of a previous Thirdness, cognitively speaking there is a limit to our perceptive abilities, which experience as undivided something that, cosmologically speaking, is in posse capable of being further divided. What is in posse belongs to cosmology. What is in actu belongs to the agent subject.
What happens when we put ourselves in the place of a perceiving subject? Zellini (2003: 26–27) reminds us that:
Adolf Grünbaum [(1969)] recently demonstrated that the measured structure of physical time justifies applying the arithmetical theory of limits to the solution of the paradox. Human awareness of time has a base limit of perceptibility, that is, a minimal threshold beyond which temporal intervals vanish into inconceivable smallness. If we consciously tried to contemplate ‘all’ the intervals of the series (a), it would be realized concretely as a countable infinity of mental acts, and the duration of each of these would be larger than the minimal threshold that time allows. But this insuperable ‘minimum’ is an Archimedean quantity: when added to itself infinite times, it yields an infinite result. Consequently, the mental contemplation of the entire series would result in an impossibly unlimited period of time. This would happen, for example, if one ‘counted’ the intervals of (a) one by one, assigning to each of them an ordinal number. This would take more time than the necessary minimum just to conceive or pronounce them. (But it is absurd, Aristotle objected [Physics 8, 8, 263a–263b], to maintain that whatever moves, moves while counting.) In reality, by raising doubts about the possibility of traversing the interval (0–1), Zeno exploits the unacceptable delay that is implied by reducing the series (a) to the corresponding mental acts of the counting process, but he fails to make clear that this process does not reproduce exactly the measurement of the physical time involved in the actual traversal.
Thus, Grünbaum finds Zeno’s argument illegitimate because it uses what is basically an inevitable confusion between two incompatible forms of thought. He explains that we do not experience the intervals into which we subdivide the traversal in any measure that corresponds to their actual nature. Rather, we derive our impression of their duration from
